[R] Discrepency between confidence intervals from t.test and computed manually -- why?
David Rossiter
rossiter at itc.nl
Wed Jan 4 09:58:51 CET 2006
I am sure there is something simple here I am missing, so please bear
with me.
It concerns the computation of the confidence interval for a population
mean.
The data are 125 measurements of Cs137 radation, a sample data set from
Davis "Statistics and Data Analysis in Geology" 3rd ed. (CROATRAD.TXT)
------------------
method 1: using textbook definitions: mean \pm se_mean * t-value
mu <- mean(Cs137); n <- length(Cs137)
se.mean <- sqrt(var(Cs137)/n)
# two-tail alphas
alpha <- c(1, 5, 10, 20)/100
# t-values for each tail
t.vals <- qt(1-(alpha/2), n-1)
# name them for the respective alpha
names(t.vals) <- alpha
# low and high ends of the confidence interval
round(ci.low <- mu - se.mean * t.vals, 2)
round(ci.hi <- mu + se.mean * t.vals, 2)
Output:
0.01 0.05 0.1 0.2
5.66 5.81 5.90 5.99
0.01 0.05 0.1 0.2
6.69 6.54 6.46 6.36
-----------------
So for the 95% confidence level I seem to get a CI of 5.81 .. 6.54
------------------
method 2: using t.test. I am not really testing for any specific mean,
I just want the confidence interval of the mean, which t.test seems to
give to me:
Input:
t.test(Cs137)
Output:
One Sample t-test
data: Cs137
t = 11.5122, df = 124, p-value < 2.2e-16 <-- not relevant
alternative hypothesis: true mean is not equal to 0 <-- not relevant
95 percent confidence interval:
5.115488 7.239712
sample estimates:
mean of x
6.1776
------------------------------
So with t.test I seem to get a CI of 5.12 .. 7.24 which is considerably
wider than the directly computed interval 5.81 .. 6.54. Perhaps I am
mis-understanding the CI which t.test is reporting?
Any help would be appreciated.
Thank you.
D G Rossiter
Senior University Lecturer
Department of Earth Systems Analysis (DESA)
International Institute for Geo-Information Science and Earth
Observation (ITC)
Hengelosestraat 99
PO Box 6, 7500 AA Enschede, The Netherlands
mailto:rossiter at itc.nl, Internet: http://www.itc.nl/personal/rossiter
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